An eclectic text is an attempted reconstruction of a lost text based on multiple sources. This is not as obscure a task as it might seem at first; as it happens, the Bible, the Iliad, Canterbury Tales and some of Shakespeare's plays are compilations of mixed sources. In some cases there are dozens or even hundreds of sources to compare, and in others only only the eclectic text itself remains, the source documents having been lost. There are many variations on this; in the case of Shakespeare's A Midsummer Night's Dream we have not only the first quarto, but also the folio, which was copied from the quarto but which includes corrections that appear to come from an authoritative (but mysterious) second source.
In the days of transcribing texts by hand or movable type, each scribe or printer would inevitably make different errors -- and often attempt to correct errors made by earlier scribes. Over time these minor changes could add up to big differences in meaning. Some cases are made even more perplexing by the possibility of there being multiple true sources, either independent transcriptions of oral tradition (e.g. The Gilgamesh Epic) or multiple drafts or editions by the original author (e.g. The Vision of Piers Plowman). Reconstruction of a lost original is often improved by using a selection of readings taken from multiple sources; the resulting edited text, constructed from multiple sources, is said to be eclectic.
The King James Bible is one of the more well-known examples of an eclectic text, along with all editions of the Bible descending from it. There are other methods of determining the 'best' text; for example, the New Testament text of the Greek Orthodox Church is based on the Byzantine text-type, which is the majority text -- the text found in the greatest number of existing Greek New Testament manuscripts.
The reconstruction and correction of ancient text is called textual criticism (AKA lower criticism). This is primarily concerned with identifying and removing transcription errors (copy-text editing) in source materials, but it also includes stemmatics (ordering variations of a text into a 'family-tree'), and eclecticism.